“Fading Gigolo” is John Turturro’s idea of an old-school Woody Allen comedy, so he wrote Allen into it.

It’s a sentimental farce that presents Turturro as a Brooklyn Jack-of-all-trades whose pal (Allen) decides that another trade this Jack, named Fioravante, would be good at is pleasing women.

Allen is Murray, one of Fioravante’s several bosses, as the younger man juggles several service-sector jobs to make ends meet in what we call “the gig economy.”

Murray runs a rare book shop, and he’s about to give up the ghost.

“Only rare people buy rare books.”

But those rare people figure the grandfatherly Murray can help them find something a little special – like a third for a planned menage a trois.

Mild-mannered Murray has to talk milder-mannered Fioravante into it. It helps that Sharon Stone was the woman doing the soliciting.

“Is he clean?” the society trophy wife wants to know. “I’m a little crazed. I just came from an AIDS benefit.”

And we’re off, with Sofia Vergara as the “trois” in that menage. Fioravante tackles this new gig with sensitivity and compassion. That’s why Murray figures there’s no harm in offering him to this lonely Orthodox rabbi’s widow he’s just met.

Avigal (Vanessa Paradis) is lonely, depressed and, Murray figures, in desperate need of a man’s touch. But how do you “help” an Orthodox woman?

“I don’t shake hands,” she says. Her culture doesn’t allow her to touch a man. Her elders watch over her like a hawk. Her Bensonhurst community even has its own NYPD-sanctioned neighborhood watch, and one of those over-zealous watchers (Liev Schreiber) watches Avigal with love, and a lot of suspicion. Even passing off Fioravante as a masseuse with hands “that bring magic to the lonely” is going to be tricky.

The ancient Allen gamely makes Murray a doting, baseball-playing father in an interracial marriage full of kids he has to keep entertained. Thirty years ago, he’d have made Murray’s “new pimp throws around the cash” scenes very “Broadway Danny Rose” and funnier.

Bob Balaban is amusing as Murray’s trusted but irritable lawyer, Vergara and Stone set off comic sparks. But Turturro winds up playing the sad straight man in his own comedy. And he and Paradis play this too somber. Sex scenes are more explicit than silly. The movie gropes around for a lighter touch.

Moments like when the Orthodox religious police nab Murray for an inquisition are meant to play like farce, but the often-scary Schreiber lends that an alarming theocratic, fascist feel. Seriously, New York allows “religious police” to enforce dogma?

But by then “Fading Gigolo” has mimicked its title and faded, a failure in tone, a romantic comic juggling act where every dropped ball kills another potential laugh in a movie that desperately needs them.